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Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject…
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This paper has been withdrawn by the author due to a serious mistake on Lemma 2.4.
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This paper has been withdrawn by the author due to a crucial error.
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This is a survey on the computational complexity of nonlinear mixed-integer optimization. It highlights a selection of important topics, ranging from incomputability results that arise from number theory and logic, to recently obtained…
It is well known that the most challenging question in optimization and discrete geometry is whether there is a strongly polynomial time simplex algorithm for linear programs (LPs). This paper gives a positive answer to this question by…
This paper has been withdrawn by the authors due to its publication
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This paper has been withdrawn by the author.